Such an electric axle drive for a motor vehicle is known from DE 10 2013 102 161 A1. In this axial drive, a first spur gear stage is provided on the electric machine side, wherein an intermediate shaft is connected as an output of this spur gear stage to a planetary carrier of the planetary gear mechanism. A ring gear of the planetary gear mechanism is connected to one spur gear of the second spur gear stage, the other spur gear thereof serving, via a differential gear mechanism, to drive two output shafts of the axle of the motor vehicle. Each output shaft is assigned a wheel, that is to say a road wheel, of this axle. The planetary gear mechanism is assigned shifting means which allow shifting under load and require that, in particular in a first gear of the motor vehicle, which is a primary gear, the transmission ratio in the planetary gear mechanism is shifted. By contrast, in the second gear, which is consequently the secondary gear, the planetary gear mechanism is shifted as a block, that is to say revolves as a block and does not lie in the power flow.